Dust 2 large sheet pans heavily with cornmeal. Set aside.
Mound 4 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add the eggs and milk mixture. Using a fork, beat together the eggs and milk mixture and begin to incorporate the flour, starting with the inner rim of the well. As you expand the well, keep pushing the flour up to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough, using the palms of both hands. Once you have a cohesive mass, remove the dough from the board, scrape up and discard any crusty bits. Lightly flour the board and continue kneading for six more minutes. The dough should be elastic and firm. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Do not skip the kneading or resting portion of this recipe, as they are essential to a light pasta.
Cut the dough into 6 equal portions and roll each into a 1-inch thick log. Run each log through a meat grinder set to the smallest extrusion size using the plunger to push the dough. As the pasta exits, cut it into 12-inch pieces and let it fall onto a prepared sheet pan. Shake the pasta in the cornmeal, gently separating the strands while rolling them in the cornmeal. Repeat with the remaining dough.
Bring about 6 quarts of water to a boil and add about 2 tablespoons salt. In a 12- to 14-inch sauté pan, combine the olive oil, anchovies and onion and cook over medium heat, stirring often to break up the anchovies, until a paste is formed, about 8-10 minutes.
Drop the noodles in the boiling water, and cook until al dente, 8-9 minutes. Drain the pasta and toss into the pan with anchovies. Add the parsley, toss through and divide among 4 serving plates. Serve immediately.